Measurement of the diffusion constant can assist the characterization of molecules and fluids. The time dependent diffusion constant can be used to characterize pore geometry, such as surface-to-volume ratio and tortuosity and it has been used to study rocks by applying pulsed or static field gradients. In these NMR measurement (using spin echo and stimulated echo for example), one diffusion time (Δ) will be preset in the pulse sequence to determine the molecular displacement over Δ, thus obtaining D(Δ). Then, a series of measurements are made with different Δ's to acquire the full curve of the time-dependent diffusion constant. Measurements of diffusion using CPMG (Carr-Purcell-Meiboom-Gill) sequence alone would result in Δ comparable to the time between the π/2 and the first π pulses.
K. J. Packer, as described in “The study of slow coherent molecular motion by pulsed nuclear magnetic resonance,” Mol. Phys. 17, 355 (1969) (incorporated by reference herein in its entirety), used NMR to monitor flow rate in the presence of a weak magnetic field gradient. Packer does not recognize that a more robust measurement may be made using a strong magnetic field gradient or that diffusion and restricted diffusion measurements may be made in the presence of a strong field gradient.
Further, the conventional methods do not account for contributions from many different pathways.
Accordingly, it is an object of the present invention to provide a method that provides information regarding molecular displacement, and in particular, diffusion and restricted diffusion of a fluid (gas or liquid) in bulk or in a porous media.